关于圆形轨道稳定性的两个问题

Two Problems about Stability of a Circular Track

质点在有心力 F=- c/ rn 作用下作圆形轨道运动 ,当 n<3时 ,轨道是稳定的。其次 ,作圆形轨道运动的质点 ,若其势能为 U(r) =- km/ rp,则当 0 <p<2时 ,轨道是稳定的。指出了 n=3和 n>3这两种情况所对应的轨道不稳定性的区别 ,并讨论了从力和势能给出的两个稳定性条件之间的联系。

If a particle moves along a circular track under the action of central force F=-c/r n,the track is stable when n<3. If the potential energy of a particle moving along a circular track is U(r)=-km/r p,the track is stable when 0<p<2.This paper points out the difference in the instability of the track under the circumstances of n=3 and n>3,and discusses the relationship between two conditions of stability respectively given by force and potential energy.